Mixed finite element analysis for generalized Darcy-Forchheimer model in porous media

Abstract We considered mixed finite element discretization of generalized Darcy–Forchheimer model in a two or three dimensional porous domain, using a piecewise constant and continuous piecewise linear finite elements. The existence, uniqueness, stability and convergence of the discrete solution are established. The error estimates for the velocity and pressure in L m and L m + 1 m respectively are obtained for any m ∈ ( 1 , 2 ] . Numerical examples are also presented to confirm the rate of convergence.

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